Equations of Circles Advanced Geometry Conic Sections Lesson 1.

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Equations of Circles Advanced Geometry Conic Sections Lesson 1

An equation for a circle with center at (h, k) and radius of r units is

Example: Write an equation for each circle described. center at (-5, -3), r =

Example: Write an equation for each circle described. center at (3, -2), d = 10

Example: Write an equation for each circle described. center at the origin, r = 11

Example: Graph

Example: Graph

Example: A circle with center at (5, 4) has a radius with endpoint (-3, 4). Write an equation of the circle.

Example: A circle with a diameter of 14 has its center in the third quadrant. The lines y = 5 and x = 4 are tangent to the circle. Write an equation of the circle.

Example: A circle with a diameter of 10 has its center in the first quadrant. The lines y = -3 and x = -1 are tangent to the circle. Write an equation of the circle.

Example: Find the radius of a circle that has equation and contains (0, 2).

Example: The equation of a circle is Determine whether the line x = -1 is a secant, a tangent, or neither of the circle. Explain.

Example: The equation of a circle is Determine whether the line is a secant, a tangent, or neither of the circle. Explain.

Example: Strategically located substations are extremely important in the transmission and distribution of a power company’s electric supply. Suppose three substations are modeled by the points D(3, 6), E( -2, 1), and F(3, -4). Determine the location of a town equidistant from all three substations and write an equation for the circle.